Understanding Maclaurin Polynomials: Exploring Substitution Techniques

[estro]

I'm trying to understand the reminder of Maclaurin polynomials

[PLAIN]http://estro.uuuq.com/0.png
[PLAIN]http://estro.uuuq.com/1.png
[PLAIN]http://estro.uuuq.com/2.png
[PLAIN]http://estro.uuuq.com/3.png
[PLAIN]http://estro.uuuq.com/4.png
Here I show few attempts to use substitution on known polynomials.

Where I'm wrong?

 

[HallsofIvy]

The only thing you are doing wrong is that you have "$R_2(x)$" and "$R_4(x)$". What you should have is $R_2(x+2)$ and $R_2(x^2+ 2)[/quote] as you do on the right.$

 

[estro]

Thank you for your response,
So this is mistake in my book?: [PLAIN]http://estro.uuuq.com/book_wrong.png

So the right way is: [PLAIN]http://estro.uuuq.com/right.png